Understanding the speed limits of parametrically pumped quantum gates

Controllable couplings between qubits are vital for realizing large-scale quantum machines. In superconducting systems, high-fidelity two-qubit gates can be performed by off-resonant parametric pumping of a non-linear element dispersively coupled to two qubits. In this scheme, the performance of fast high-fidelity gates requires strong pumping. However, high drive strengths may activate unwanted transitions which can ruin gate fidelity and coherence properties. Moreover, strong coupling between the pump port and the non-linear mode may limit the lifetime of the quantum modes being controlled. In this work we will use our previously built quantum state router [Zhou and Lu, arxiv: (2021)] and a new 4-qubit quantum module as platforms (which both operated via 3-wave-based parametric gates) to study how to characterize and control the factors that limit our gate speed. We show how to identify and mitigate the effects of parasitic parametric processes while maintaining qubit lifetimes, and engineer the drive port's impedance to allow stronger parametric drives while maintaining mode lifetimes. In total, our results open a pathway to realizing a modular qubit architecture featuring high-fidelity parametric gates.